Non-classical higher-order photon correlations with a quantum dot strongly coupled to a photonic-crystal nanocavity

We use the third- and fourth-order autocorrelation functions $g^{(3)}(tau_1,tau_2)$ and $g^{(4)}(tau_1,tau_2, tau_3)$ to detect the non-classical character of the light transmitted through a photonic-crystal nanocavity containing a strongly-coupled quantum dot probed with a train of coherent light pulses. We contrast the value of $g^{(3)}(0, 0)$ with the conventionally used $g^{(2)}(0)$ and demonstrate that in addition to being necessary for detecting two-photon states emitted by a low-intensity source, $g^{(3)}$ provides a more clear indication of the non-classical character of a light source. We also present preliminary data that demonstrates bunching in the fourth-order autocorrelation function $g^{(4)}(tau_1,tau_2, tau_3)$ as the first step toward detecting three-photon states.